Day 174 · Jun 22

Birthday of Hermann Minkowski (1864)

Hermann Minkowski — Einstein's former mathematics professor — reformulated special relativity in 1907 as geometry in four-dimensional space-time. In Minkowski space, the separation between events is ds² = c²dt² − dx² − dy² − dz² — a geometry with an unusual minus sign that distinguishes time from space. This makes the mathematics of special relativity geometric and transparent. Einstein initially resisted this formulation, then adopted it completely. Minkowski also proved fundamental results in the geometry of numbers, including a theorem that guarantees every sufficiently large symmetric body contains a non-zero lattice point.

In Minkowski space-time, two events with zero separation are connected by light — nothing else. What does it mean geometrically for a path to have zero space-time length?

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